Explore the words cloud of the GEOGRAL project. It provides you a very rough idea of what is the project "GEOGRAL" about.
The following table provides information about the project.
INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
|Coordinator Country||Poland [PL]|
|Total cost||146˙462 €|
|EC max contribution||146˙462 € (100%)|
1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
|Duration (year-month-day)||from 2015-09-01 to 2017-08-31|
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|1||INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK||PL (WARSZAWA)||coordinator||146˙462.00|
The aim of GEOGRAL is to strengthen the bonds of the geometric theory of nonlinear PDEs (and, in particular, integrable systems and equations of Monge-Ampère type) with the geometry of Lagrangian Grassmannians and their submanifolds. In spite of the evident parallelism between these two disciplines, attempts have been rare, yet sophisticated, to cast a bridge between them, and the Applicant himself already gave his own contribution in this direction: he clarified the structure of the space of non-maximal integral elements of the contact planes in jet spaces and studied 3rd order Monge-Ampère equations (which turn out to be of key relevance in topological field theories) through the so-called meta-symplectic structure on the 1st prolongation of a contact manifold. GEOGRAL has a wide applicative scope, as its theoretical results can be tested on equations and variational problems of key importance for Natural Sciences, Technology and Economy. Tailored to the Applicant's scientific profile and designed in continuity with his previous and current research activities, GEOGRAL consists of four research lines: [MOV] Regard Lagrangian Grassmannians as homogeneous spaces and and use Cartan's method of moving frame to classify their submanifolds, as in D. The's work, and characterise the corresponding invariant equations, in continuity with D. Alekseevsky's work. [HYD] Continue the study of certain rational normal curve bundles on Lagrangian Grassmannians, and their bisecant varieties, which are associated with integrable systems of hydrodynamic type, discovered by E. Ferapontov. [HMA] Geometric study of multi-dimensional and higher-order Monge-Ampère equations, initiated by G. Manno and the Applicant. [FBV] Study some examples of Cauchy problems and variational problems with free boundary values by exploiting the geometric structures on the spaces of isotropic flags and non-maximal isotropic elements of a meta-symplectic space, in continuity with the Applicant's own work.
|year||authors and title||journal||last update|
A. J. Bruce, K. Grabowska, G. Moreno
On a Geometric Framework for Lagrangian Supermechanics
published pages: , ISSN: 1941-4889, DOI:
|Journal of Geometric Mechanics||2019-07-23|
Giovanni Moreno, Monika Ewa Stypa
Geometry of the free-sliding Bernoulli beam
published pages: , ISSN: 1804-1388, DOI: 10.1515/cm-2016-0011
|communications in mathematics 2 issues/vol./yr.||2019-07-23|
An introduction to completely exceptional 2nd order scalar PDEs
published pages: , ISSN: , DOI:
Gianni Manno, Giovanni Moreno
Meta-Symplectic Geometry of 3 rd Order Monge-AmpÃ¨re Equations and their Characteristics
published pages: , ISSN: 1815-0659, DOI: 10.3842/SIGMA.2016.032
|Symmetry, Integrability and Geometry: Methods and Applications||2019-07-23|
Jan Gutt, Gianni Manno, Giovanni Moreno
Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution
published pages: , ISSN: 0393-0440, DOI: 10.1016/j.geomphys.2016.04.021
|Journal of Geometry and Physics||2019-07-23|
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